On Intersection with Tori

In 2006, a bad field was constructed (together with Baudisch, Hils and Wagner) collapsing Poizat's green fields. In this talk, we will not concentrate on the general methodology for collapsing specific structures, but more on a specific result in algebraic geometry, a weaker version of the Conjecture on Intersection with Tori (CIT). We will present a model theoretical proof of this result as well as discuss the possible generalizations to positive characteristic. We will try to make the talk  self-contained and aimed for an audience with a basic acquaintance with Model Theory.